Scan Conversion

1. Scan Conversion Jehee Lee Seoul National University

2. Attributes of Output Primitives • Handling attribute parameters • Passing a list of attributes as a parameter of output primitive functions • Eg) X-windows • Maintain the “current” values of attributes and provide with a set of function for attribute settings • Eg) OpenGL • Maintain a scene graph and attribute nodes affects descending primitive nodes • Eg) Open Inventor

3. Line Attributes Butt cap Round cap Projecting square cap Miter join Round Join Bevel join

4. Area Filling How can we generate a solid color/patterned polygon area?

5. How to decide interior -Parity Fill Approach • For each pixel determine if it is inside or outside of a given polygon. • Approach • from the point being tested cast a ray in an arbitrary direction • if the number of crossings is odd then the point is inside • if the number of crossings is even then the point is outside

6. How to decide interior -Parity Fill Approach • Very fragile algorithm • Ray crosses a vertex • Ray is coincident with an edge • Commonly used in ECAD • Suitable for H/W

7. How to decide interior-Winding Number A winding number is an attribute of a point with respect to a polygon that tells us how many times the polygon encloses (or wraps around) the point. It is an integer, greater than or equal to 0. Regions of winding number 0 (unenclosed) are obviously outside the polygon, and regions of winding number 1 (simply enclosed) are obviously inside the polygon. • Initially 0 • +1: edge crossing the line from • right to left • -1: left to right • use cross product of line and • edge vectors • No cross vertices

8. Area Filling (Scan line Approach) • Take advantage of • Span coherence: all pixels on a span are set to the same value • Scan-line coherence: consecutive scan lines are identical • Edge coherence: edges intersected by scan line i are also intersected by scan line i+1

9. Area Filling (Scan line Approach) • For each scan line (1) Find intersections (the extrema of spans) • Use Bresenham's line-scan algorithm (2) Sort intersections (increasing x order) (3) Fill in between pair of intersections

10. Area Filling (Scan line method)

11. Area Filling(Filling Methods) • Pixel Adjacency • Boundary-Fill Algorithm • starting a point inside he figure and painting the interior in a specified color or intensity. 4-connected 8-connected

12. Boundary Filling

13. Boundary Filling • Efficiency in space! • finish the scan line containing the starting position • process all lines below the start line • process all lines above the start line

14. Flood Filling : Start a point inside the figure, replace a specified interior color only.

15. Problems of Filling Algorithm • What happens if a vertex is shared by more than one polygon, e.g. three triangles? • What happens if the polygon intersects itself? • What happens for a “sliver”? • Solutions? • Redefine what it means to be inside of a triangle • Different routines for nasty little triangles

16. Aliasing in CG Which is the better?

17. Aliasing in CG • Digital technology can only approximate analog signals through a process known as sampling • The distortion of information due to low-frequency sampling (undersampling) • Choosing an appropriate sampling rate depends on data size restraints, need for accuracy, the cost per sample… • Errors caused by aliasing are called artefacts. Common aliasing artefacts in computer graphics include jagged profiles, disappearing or improperly rendered fine detail, and disintegrating textures.

18. The Nyquist Theorem the sampling rate must be at least twice the frequency of the signal or aliasing occurs

19. Aliasing Effects

20. Artefacts - Jagged profiles • Jagged silhouettes are probably the most familiar effect caused by aliasing. • Jaggies are especially noticeable where there is a high contrast between the interior and the exterior of the silhouette

21. Artefacts - Improperly rendered detail

22. Artefacts - Disintegrating textures • The checkers should become smaller as the distance from the viewer increases.

23. Antialiasing • Antialiasing methods were developed to combat the effects of aliasing. The two major categories of antialiasing techniques are prefiltering and postfiltering.

24. Prefiltering • Before sampling the image, use a low-pass filter to eliminate frequencies above the Nyquist limit • This blurs the image, but ensures that no high frequencies will be misrepresented as low frequencies • Determines pixel intensity based on the amount that a particular pixel is covered by an object in the scene. Determining such areas requires extensive calculations and integral approximations

25. High Frequency

26. Basis for Prefiltering Algorithms

27. A2 A1 AB A3 Catmull’s Algorithm • Find fragment areas • Multiply by fragment colors • Sum for final pixel color

28. Prefiltering Example

29. Postfiltering • Postfiltering, also known as supersampling • For each displayed pixel, a postfiltering method takes several samples from the scene and computes an average of the samples to determine the pixel's color. • Doesn’t eliminate aliasing, just shifts the Nyquist limit higher • Can’t fix some scenes (e.g., checkerboard) • Relatively easy and often works all right in practice • Can be added to a standard renderer : A-buffer

30. Postfiltering • The two steps in the postfiltering process are: 1. Sample the scene at n times the display resolution. 2. The color of each pixel in the rendered image will be an average of several samples. • A filter provides the weights used to compute the average.

31. Sampling in the Postfiltering method • Supersampling from a 4*3 image. • Sampling can be done randomly or regularly. The method of perturbing the sample positions is known as "jittering."

32. Nonuniform Supersampling Adaptive Sampling

33. Problem: Many more blue samples than white samples But final pixel actually more white than purple! Simple filtering will not handle this correctly Adaptive Sampling Final Samples

34. Filters

35. Antialiasing http://www.siggraph.org/education/materials/HyperGraph/aliasing